Pregnancies occurring after a rape, Mourdock said, were intended by God.

"I don't know how these guys come up with these ideas," Obama told Leno. "Let me make a very simple proposition: Rape is rape. It is a crime. And so these various distinctions about rape don't make too much sense to me -- don't make any sense to me."

Mourdock has apologized for offending anyone. But his words have fueled the national fight to gain women voters in a very close presidential election. Related: Women voters by the numbers

During his chat with Leno, Obama used the Mourdock controversy to say that the next president likely would appoint a new Supreme Court justice who could potentially change federal abortion laws.

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Obama's GOP presidential rival, Mitt Romney, has said he would appoint justices who would support overturning Roe vs. Wade, the 1973 court decision affirming a woman's right to have an abortion.

"Roe vs. Wade is probably hanging in the balance," Obama said.

"Women are capable of making these decisions in consultation with their partners, with their doctors," said the president. "And for politicians to want to intrude in this stuff often times without any information is a huge problem."

The Obama campaign released a new television ad reinforcing those points, highlighting Romney comments on Roe vs. Wade and his plan to try and cut funding for Planned Parenthood.

Reaction within Mourdock's own party has been deafening. Romney had endorsed him in a TV ad before the controversy. Afterward, Romney said through a campaign spokeswoman that he did not agree with Mourdock's comments, but the ad would continue to run.

Other powerful Republicans distancing themselves from Mourdock include 2008 GOP presidential nominee Sen. John McCain and Texas Sen. John Cornyn, a top GOP Senate fundraiser.

Sen. Kelly Ayotte, R-New Hampshire, canceled plans to campaign with Mourdock on Wednesday. And in a sharp rebuke, a fellow Republican running for Indiana's governor seat, former Rep. Mike Pence, issued a statement saying, "I strongly disagree with the statement made by Richard Mourdock during last night's Senate debate. I urge him to apologize."

A senior Republican strategist said Mourdock may not face as much push-back from GOP leaders for two reasons: Republicans very much want to hold on to that Indiana Senate seat. That -- with less than two weeks remaining before Election Day.

"I struggled with it myself for a long time, but I came to realize life is a gift from God, and I think even when life begins in that horrible situation of rape, that it is something that God intended to happen," said Mourdock, who now serves as Indiana's state treasurer. He also said he would allow for exceptions to an abortion ban when a mother's life was in danger.

GOP Senate candidate: Pregnancies from rape God's will

On Wednesday, Mourdock tried to clarify his comments, saying, "I absolutely abhor violence. I absolutely abhor any kind of sexual violence. I abhor rape, and I am absolutely confident that, as I stand here, the God that I worship abhors violence, abhors sexual violence and abhors rape. The God that I worship would never, ever want to see evil done."

Sounds familiarIt's not the first time rape and abortion have dominated the campaign.

In August, Rep. Todd Akin of Missouri, who's also a Republican running for Senate, ignited a firestorm when he said "legitimate rape" rarely resulted in pregnancy.

And last week, GOP Rep. Joe Walsh, who's running for re-election in Illinois, questioned the necessity of allowing abortions if a mother's life is at risk. He said such an exemption to an abortion ban was simply a political tool used by pro-choice activists.

Doctors strongly disputed Rep. Walsh¹s contention that doctors rarely, if ever, perform abortions to save the life of the mother.

McCain, R-Arizona, told CNN on Wednesday that his support for Mourdock was dependent on an apology. "It depends on what he does," McCain said on "Anderson Cooper 360."

Thursday, after hearing of Mourdock's apology, McCain said that he "is glad" Mourdock apologized and "hopes the people of Indiana will elect Mr. Mourdock."

"What the Senate candidate said is the child is a gift from God, whether it's conceived from rape or not, it's still -- the gift of human life is a gift from God," Santorum explained. "He didn't say rape was a gift from God. You'd have to contort words beyond meaning to get that understanding of it."

It was "gotcha politics," Santorum said, because Mourdock was "talking about the baby in the womb as something that is precious," even though it was conceived through "horrible circumstances."

The whole thing is "outrageous" and "demeaning to women," said Democratic National Committee Chairwoman Debbie Wasserman Schultz in a statement.

Party leaders called on Romney to stop airing his TV ad endorsing Mourdock.

"As Mourdock's most prominent booster and star of Mourdock's current campaign ads, Mitt Romney should denounce these comments more strongly than he has," DNC spokesman Brad Woodhouse said. "He should go further and demand that the ad featuring him speaking directly to the camera on Mourdock's behalf be taken off the air, and Mitt Romney should withdraw his endorsement of Mourdock immediately."